In shrouded rotor applications, it is frequently the case that spinning rotor blades are operated at exceptionally high rotational velocity. From an aerodynamic standpoint, high rotational velocities are not a particular concern when dealing with small diameter rotors. However, with larger diameter rotors, such as typically found in turbofan jet engines and steam turbines, large angular velocities can result in linear velocities at radially extended locations, e.g., at the rotor blade tips, which approach and even exceed the speed of sound in the particular fluid medium. These high local velocities at the tips of the rotor blades which approach or exceed the speed of sound are associated with an increase in drag due to a reduction in the total pressure through shock waves and due to thickening and even separation of the boundary layer due to the local but severe adverse pressure gradients caused by the shock waves.
In many shrouded rotor applications, e.g., the fan section of an axial flow turbofan jet engine, the rotor blades are stiffened by part-span dampers which circumferentially interconnect adjacent rotor blades thereby encircling the hub from which the rotor blades extend. Since many such shrouded rotor applications operate at exceptionally high rotational velocities, these large diameter rotor blades have a tendency to untwist as a result of the air pressures generated. In these instances, part-span dampers are particularly useful in rigidifying the rotor blades and dampening vibration. Typically, the part-span dampers are located between one-half and two-thirds distance from the hub.
When the shrouded rotor is operated at transonic speeds, i.e., the linear velocity of the rotor blades relative to the freestream approaches and exceeds Mach 1.0, the physical presence of the part-span dampers in the flow path between the hub and the casing surrounding the rotor blades increases shock wave drag. Such drag has the net effect of reducing fuel efficiency in the case of turbofan jet engines. In such applications, approximately 50% of the available energy produced in the combustion process is required to operate the compressor section and large bypass fan section. Therefore, it will be appreciated that a reduction in shock wave drag will have a considerable effect on engine efficiencies.
It has been indicated that to minimize drag losses caused by the part-span dampers, several things should be taken into consideration. First, the leading and trailing edges of the part-span dampers should be as sharp as possible. Second, the part-span dampers should be located as near to the hub as possible to minimize shock losses. Third, work input should be minimized at the part-span damper location. Fourth, the part-span damper should be as thin as possible to minimize the area influenced. However, even after all of these design considerations have been implemented, there remains a part-span damper of some size in some location along the rotor blades that causes additional profile and shock losses simply due to its physical presence. Accordingly, there remains incentive for further optimization of the rotor/part-span damper combination to minimize losses at transonic speeds.
A fruitful area of past research in transonic aerodynamics has included the well-known Area Rule. Heretofore, the Area Rule has only been applied in external flow situations where a drag reduction for wing/body combinations has been realized, as originally proposed by Richard T. Whitcomb in "A Study of the Zero-Lift Drag-Rise Characteristics of Wing-Body Combinations Near the Speed of Sound", NACA TR 1273, 1952. The theories of transonic and supersonic flow with small disturbances were extended in a very practical way by Whitcomb in his development of the Area Rule. The Area Rule aims at arranging the airplane components so that the total aircraft cross-sectional area, in planes perpendicular (normal) to the line of flight, has a smooth and prescribed variation. The designing of a fuselage with variable diameter for transonic drag reasons is sometimes called "coke-bottling".
The Area Rule, more particularly, states that all aircraft having the same longitudinal distribution of cross-sectional area in planes normal to the flight direction, including the wings, fuselage, nacelles, tail surfaces, or any other components, will have the same wave drag at zero lift. Thus, a complex airplane will have the same zero-lift wave drag as a body of revolution whose cross-sectional area is the same at corresponding longitudinal locations. Although Whitcomb's Area Rule has been successfully applied in external flow conditions for several decades, the prior art has never considered applying the Area Rule to the flow through rotating blades in an axial flow shrouded rotor section.